Optimal Computing Budget Allocation for regression with gradient information

Abstract

We consider the problem of optimizing the performance of a stochastic system, e.g., a discrete-event system, where the system performance is evaluated using stochastic simulations. Our objective is to allocate simulation budget to maximize the probability of correct selection (PCS) of the best design, where both system performance and gradient information can be obtained simultaneously via simulation. The objective function is assumed to be quadratic, or can be approximated by a quadratic regression model. The main contribution of our work is to utilize gradient information to enhance the efficiency of traditional Optimal Computing Budget Allocation (OCBA). We develop near-optimal rules that determine design points where simulations should be run and the number of runs allocated to each point. Our numerical experiments demonstrate that the proposed approach performs much better than other existing ranking and selection methods, even in cases where derivative information is very noisy and its simulation cost is high.